The present invention relates to the field of data communications, and more particularly to evaluating bit error rates for data communication systems.
The bit error rate (BER) of an information transport system is a measure of quality, indicating what percentage of data bits applied as input to the system are correctly retrieved at the output.
The BER of an actual data communication system can be determined by measuring the output of the system for all possible inputs. This requires a large number of measurements of an existing system, yet still may not yield a result which can be generalized over variations of the system. In practice, therefore, the BER is more often predicted from known or presumed characteristics of the system.
In order to predict the BER, a system for which BER is to be estimated is generally modeled using a modeling program such as MATLAB(trademark). MATLAB(trademark) is a general purpose mathematical program, with features for system modeling and simulation, and allows the designer to make various operating assumptions as a basis for any particular set of predictions. A faster simulation program, such as the FAST simulator described in xe2x80x9cA Methodology for Efficient High-Level Dataflow Simulation of Mixed-Signal Front-Ends of Digital Telecom Transceivers,xe2x80x9d by G. Vandersteen, P. Wambacq, Y. Rolain et al., (Proc. DAC 2000), may be used to reduce simulation time. Faster simulation is also taught in U.S. patent application Ser. No. 09/591,026.
Modern communication systems generally use a symbol set for transmitting data electromagnetically, and a BER estimate for a system must be based on the anticipated symbol set which will be used. In a typical Monte Carlo simulation, a symbol will be selected at random and the signal representing that symbol then will be sent through the simulator. (The term xe2x80x9csignalxe2x80x9d is for some purposes herein used interchangeably with the xe2x80x9csymbolxe2x80x9d which the signal represents.) The simulated xe2x80x9creceived dataxe2x80x9d will be compared with the actual data represented by the symbol. For low BER systems, this will most often show no error. The simulation will then be run repetitively, until a probability of error can be determined (generally requiring that at least one error be observed). This can take a great deal of computing effort.
The above estimation of the probability of error for a given symbol is generally then be done for a large portion of the total symbols used by the system, in order to accurately predict the BER. The lower is the probability of error for a particular symbol, generally the more simulations are necessary to determine the error probability. This method requires extremely large amounts of calculation to accurately determine BER for a complex system having a large symbol set.
Schoukens et al., xe2x80x9cParametric and Nonparametric Identification of Linear Systems in the Presence of Nonlinear Distortionsxe2x80x94a Frequency Domain Approach,xe2x80x9d IEEE Trans. on Automatic Control, Vol. 43, No. 2, February 1998 (Reference [1]) demonstrates that the response of a nonlinear system which is excited by a multi-tone (e.g. OFDM) signal can be approximated by a xe2x80x98best linear approximationxe2x80x99, together with an additive noise source. This reference shows that this xe2x80x98best linear approximationxe2x80x99 and the noise source represent the average behavior of the nonlinearity for a particular set of signals.
It is known to use quasi-analytical methods for predicting BER. Jeruchim et al., xe2x80x9cSimulation of Communication Systems,xe2x80x9d Plenum Press, New York, 1992 (Reference [2]) and Santella, et al., xe2x80x9cA Hybrid analytical-simulation procedure for performance evaluation in M-QAM-OFDM schemes in presence of nonlinear distortions,xe2x80x9d IEEE Transactions on Vehicular Technology Vol. 47, no. 1, February 1998 pp. 142-151 (Reference [3]) both show such quasi-analytical methods for predicting BER. When applied, as suggested, for the whole set of possible input signals, the bit error rate determined is far from accurate, because the assumption underlying the quasi-analytical method are more violated when the method is applied to a wide range of signals. This is particularly so for BER prediction techniques applied to signals and systems which suffer from clipping. Thus, what is needed is a method which accurately predicts BER, for systems including those which suffer from signal clipping, without imposing the computing burden of Monte Carlo techniques.
Muller et al., xe2x80x9cOFDM with Reduced Peak-to-Average Power Ratio by Multiple Signal Representation,xe2x80x9d Annals of Telecommunications, Vol. 52, nos. 1-2, pp. 58-67, February 1997 (Reference [4]) and Bauml et al., xe2x80x9cReducing the Peak-to-Average Ratio of Multicarrier Modulation by Selected Mapping,xe2x80x9d Electronics Letters, Vol. 22, pp. 2056-2057, October 1996 (Reference [5]) disclose analytical approximation of the probability, within an entire signal set, of signal subsets having common characteristics. In particular, these references disclose approximations of the probability of signal sets distinguished according to the crest factor (CF) of their representative signals. Such analytical approximations are also inaccurate, because again the underlying assumptions are violated for the signals under consideration. Hence, a method to avoid the inaccuracy of known analytical approximation techniques is needed.
The present invention addresses the above-noted need by applying a combination of Monte Carlo and quasi-analytical techniques to systems. A plurality of subsets of the possible signals which the system will produce are separately evaluated for their contribution to BER, and all of the separate contributions are then appropriately combined. Known analytical approximation techniques are applied only to part of the CF distribution, while a Monte Carlo approach is more appropriately applied for another part of the CF distribution. Signals representing a significant portion of the total signal set of a system (based on its symbol set) are each evaluated. The evaluated signals will be divided into signal subset groups according to relevant characteristics, particularly characteristics which reflect a tendency of the signal to impair the accuracy of quasi-analytical methods. For example, the crest factor (CF) of a signal (the ratio of the peak value of the signal to its rms power value) is a characteristic which is related to a tendency to cause inaccuracies in quasi-analytical BER estimations. A decision is made whether to evaluate the BER contribution of that particular signal by Monte Carlo simulation, or by one of a plurality of quasi-analytical approaches.
For each signal subset, an appropriate method is selected by which to evaluate a BER which the system would have using only signals of that signal subset. In particular, BER for the subset may be determined using Monte Carlo simulations, or by a quasi-analytical approach (or by one of a plurality of quasi-analytical approaches). Then, a representative sample of signals from each subset is selected, and a BER predicted for that signal subset according to the method chosen.
The probability of occurrence of the subset of signals (as compared to the entire signal set) is evaluated. The system BER is predicted by combining the contribution of each signal subset.